Is this argument formally valid?

Question: Is this argument formally valid!?

Hi all, just wondering if this form of argument is valid/strong:

P1!. x is y!.
P2!. p is not y!.
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C!. p is not x!.

Just worried about basing an assignment thats worth 30% of my mark on it without confirmation!. Thanks!Www@QuestionHome@Com

Best Answer - Chosen by Asker:

P1: If X then Y
P2: If P then ~Y
C: If P then ~X

Assuming that all three statements are universal statements (as shown above), then yes!.

The contrapositive of P1 is 'If ~Y then ~X'
Taking this contrapositive together with P2, the conclusion follows!.

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I disagree with Jack!. 'X is Y' is properly quantified as 'All X are Y", not 'All Y are X'!. These are not equivalent statements, and if the latter is used, the argument is invalid!.
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I disagree with Einstein!. While it is true that 'p is not y' does not exclude 'p from being x', 'p is not y' is only one premise!. When the other premise is equivalent to 'not y is not x', then the conjunction of the two premises does exclude 'p from being x'!.
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I disagree with virgil!. 'All X are Y' does not imply that 'All Y are X' (or, 'y would also have to be x', as you put it)!. To make such an inference is to commit the fallacy of illicit conversion!.Www@QuestionHome@Com

yes!. assuming that x is always y, y would also have to be x!. so for p to be one and not the other is impossibleWww@QuestionHome@Com

The best way phrase it is:

All Y's are X's!.
P is not Y
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C!. P is not X!.Www@QuestionHome@Com

No!. The fact that p is not y does not exclude it from being x!.
Unlike my learned friend I do not make asssumptions!.Www@QuestionHome@Com

yes, it is valid!.!.!.!.
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